Essentially Optimal Robust Secret Sharing with Maximal Corruptions

Bishop, Allison; Pastro, Valerio; Rajaraman, Rajmohan; Wichs, Daniel

doi:10.1007/978-3-662-49890-3_3

Cited by 22 publications

(46 citation statements)

References 14 publications

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“…Since the keys k i are independent random variables, it follows that the individual events in the intersection are independent as well, and each happens with probability at most a |K| , see [2,Claim 2.5]. Hence, the intersection of the events happens with probability at most (a/|K|) η , proving the proposition.…”

Section: Proposition 23mentioning

confidence: 80%

“…As part of a protocol for robust secret sharing, [2] introduced the notion of a 'robust distributed storage'. Their method for achieving this can easily be converted to a one-round protocol for RMT.…”

Section: A Methods Based On List-decodingmentioning

confidence: 99%

“…In particular, we use a hash family based on polynomial evaluation similar to the one used in [2], but generalized to evaluate in several points.…”

Section: Definition 21mentioning

confidence: 99%

“…Rewriting (3) in the same way, and substituting the aforementioned values of L and s, we see that this inequality is satisfied as well. Thus, Protocol 1 is capable of sending messages of length a = ⌊︁ n 5 ⌋︁ + 1 rather than a = ⌊︁ n 8 ⌋︁ + 1 as in [2]. The output list is 5 codewords in this case.…”

Section: Theorem 41mentioning

confidence: 99%

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On one-round reliable message transmission

Christensen

2019

Information Processing Letters

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In this paper, we consider one-round protocols for reliable message transmission (RMT) when t out of n = 2t + 1 available channels are controlled by an adversary. We show impossibility of constructing such a protocol that achieves a transmission rate of less than Θ(n) for constant-size messages and arbitrary reliability parameter. In addition, we show how to improve two existing protocols for RMT to allow for either larger messages or reduced field sizes. Related workRMT has also been studied in [9,10]. The protocol in [10] is based on listdecoding of folded Reed-Solomon codes, but although it attains the optimal transmission rate, the computational cost for the receiver to recover the message is exponential in the number of channels. The work [9] contains bounds and constructions for both the secure and the reliable-only settings. In addition, they achieve this while tolerating a mixed adversary, giving more fine-grained control of the adversarial assumptions.Although this paper is only concerned with RMT, we also direct the reader to related works on secure message transmission; that is, protocols that also offer privacy. This additional guarantee comes at a cost. As shown by [3], perfect security for n = 2t + 1 requires at least two rounds, and a single-round protocol can only offer security in the case n ≥ 3t + 1. In the former setting, Agarwal et al.[1] gave a perfectly secure two-round protocol that achieves optimal performance asymptotically, albeit at a high computational cost. A computationally efficient protocol was subsequently achieved by Kurosawa and Suzuki [8] using the concept of pseudobases. This idea was also taken up by [11], who obtained further improvements, reducing the minimally required message size from O(n 2 log n) to O(n log n).The setting where privacy is perfect, but reliability is not, was initially handled by [4] under the assumption that channels support multicast. The proposed solution, however, was inefficient for certain values of t and n. This was rectified in [13], where an efficient protocol for these values was given. Preliminaries Model assumptionsWe assume that Alice and Bob are connected via n = 2t + 1 simple channels, meaning that the channels allow both Alice and Bob to transmit data, but

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Section: Proposition 23mentioning

confidence: 80%

Section: A Methods Based On List-decodingmentioning

confidence: 99%

“…In particular, we use a hash family based on polynomial evaluation similar to the one used in [2], but generalized to evaluate in several points.…”

Section: Definition 21mentioning

confidence: 99%

Section: Theorem 41mentioning

confidence: 99%

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On one-round reliable message transmission

Christensen

2019

Information Processing Letters

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“…Message sharing schemes [23][24][25][26] are good methods for EMRs' cross-institutional exchange, which can guarantee the messages' security and integrity through the delivery processes between the users, the healthcare blockchain system, and the consumer. The first message sharing scheme was proposed by Shamir [24], which was constructed with a threshold access structure in which an original message can be divided into n shares and recovered by at least t(1 < t ≤ n) shares.…”

Section: Message Sharing Schemesmentioning

confidence: 99%

Privacy-Preserving in Healthcare Blockchain Systems Based on Lightweight Message Sharing

Cai

2020

Sensors

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Electronic medical records (EMRs) are extremely important for patients’ treatment, doctors’ diagnoses, and medical technology development. In recent years, the distributed healthcare blockchain system has been researched for solving the information isolated island problem in centralized healthcare service systems. However, there still exists a series of important problems such as the patients’ sensitive information security, cross-institutional data sharing, medical quality, and efficiency. In this paper, we establish a lightweight privacy-preserving mechanism for a healthcare blockchain system. First, we apply an interleaving encoder to encrypt the original EMRs. This can hide the sensitive information of EMRs to protect the patient’s privacy security. Second, a ( t , n )-threshold lightweight message sharing scheme is presented. The EMRs are mapped to n different short shares, and it can be reconstructed by at least t shares. The EMR shares rather than the original EMRs are stored in the blockchain nodes. This can guarantee high security for EMR sharing and improve the data reconstruction efficiency. Third, the indexes of the stored EMR shares are employed to generate blocks that are chained together and finally form a blockchain. The authorized data users or institutions can recover an EMR by requesting at least t shares of the EMR from the blockchain nodes. In this way, the healthcare blockchain system can not only facilitate the cross-institution sharing process, but also provide proper protections for the EMRs. The security proof and analysis indicate that the proposed scheme can protect the privacy and security of patients’ medical information. The simulation results show that our proposed scheme is more efficient than similar literature in terms of energy consumption and storage space, and the healthcare blockchain system is more stable with the proposed message sharing scheme.

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Towards Optimal Robust Secret Sharing with Security Against a Rushing Adversary

Fehr

Yuan

2019

Lecture Notes in Computer Science

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Robust secret sharing enables the reconstruction of a secretshared message in the presence of up to t (out of n) incorrect shares. The most challenging case is when n = 2t + 1, which is the largest t for which the task is still possible, up to a small error probability 2 −κ and with some overhead in the share size. Recently, Bishop, Pastro, Rajaraman and Wichs [3] proposed a scheme with an (almost) optimal overhead of O(κ). This seems to answer the open question posed by Cevallos et al. [6] who proposed a scheme with overhead of O(n + κ) and asked whether the linear dependency on n was necessary or not. However, a subtle issue with Bishop et al.'s solution is that it (implicitly) assumes a non-rushing adversary, and thus it satisfies a weaker notion of security compared to the scheme by Cevallos et al. [6], or to the classical scheme by Rabin and BenOr [13]. In this work, we almost close this gap. We propose a new robust secret sharing scheme that offers full security against a rushing adversary, and that has an overhead of O(κn ε), where ε > 0 is arbitrary but fixed. This n ε-factor is obviously worse than the polylog(n)-factor hidden in the O notation of the scheme of Bishop et al. [3], but it greatly improves on the linear dependency on n of the best known scheme that features security against a rushing adversary (when κ is substantially smaller than n). A small variation of our scheme has the same O(κ) overhead as the scheme of Bishop et al. and achieves security against a rushing adversary, but suffers from a (slightly) superpolynomial reconstruction complexity.

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Essentially Optimal Robust Secret Sharing with Maximal Corruptions

Cited by 22 publications

References 14 publications

On one-round reliable message transmission

On one-round reliable message transmission

Privacy-Preserving in Healthcare Blockchain Systems Based on Lightweight Message Sharing

Towards Optimal Robust Secret Sharing with Security Against a Rushing Adversary

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